Wadge [1]} introduced games on subsets \(A,B\subseteq {{N}}^{{N}}\)  to characterize the reducibility that is named after him.
Nobrega and Pauly [2]}, [3]} have used a modification of Wadge games for problems \(f:\subseteq X\rightrightarrows Y\)  in order to characterize lower cones in the Weihrauch lattice.
We consider similar generalizedWe warn the reader that the extension of the notion of a Wadge game from sets \(A,B\subseteq {{N}}^{{N}}\) 
to problems does not automatically mean that determinacy properties carry over. versions of Wadge and Lipschitz games, defined as follows. We recall that by \({f^\mathrm {r}:\subseteq {{N}}^{{N}}\rightarrow {{N}}^{{N}}}\)  we denote the realizer version
of a problem \(f:\subseteq X\rightrightarrows Y\)  (see section ).
